Integer palindrome checker

An integer palindrome is a whole number that reads identically from left to right and from right to left. Classic classroom examples include zero, seven, eleven, one hundred twenty-one, three thousand four hundred forty-three, and twelve thousand three hundred twenty-one. Counterexamples include ten, one hundred, one hundred twenty-three, and every negative integer, because the leading minus sign is part of how the number is read and does not match a trailing digit. This checker accepts one integer, extracts its decimal digits with a deterministic half-reversal loop, and returns true or false together with the signed form, the unsigned digit string, and the reversed digits so you can audit the verdict by eye.

What it means for an integer to be a palindrome

Write the integer in ordinary base-ten form, including a leading minus sign when the number is negative. That character string is the reading. The number is a palindrome when the reading equals its own reverse: the first character matches the last, the second matches the second-to-last, and so on.

Single-digit non-negative integers are always palindromes, because a one-character string equals itself. Zero is a palindrome. Eleven, twenty-two, and every other two-digit number whose tens digit equals its units digit are palindromes.

One hundred twenty-one and three thousand four hundred forty-three are the usual textbook three-digit and four-digit examples. Ten is not a palindrome: its reading is one-zero and the reverse is zero-one, which is a different string and would also be a different integer if leading zeros were allowed. One hundred is not a palindrome for the same reason.

Negative one hundred twenty-one is not a palindrome either, even though its absolute value is: the signed reading is minus-one-two-one and the reverse is one-two-one-minus. This page answers a yes-or-no question about one decimal integer. It does not list other bases in which the same integer might become palindromic, and it does not treat a word, a date, or a sentence as the input.

The definition is fixed and deterministic. There is no sampling, no floating-point comparison, and no approximate equality. A non-integer is not classified as false; it is rejected, because the contract is about whole numbers only.

How the input is read and how the half-reversal stays exact

Internally the engine does not convert the number to a string in order to decide the flag. It runs a half-reversal on the non-negative magnitude: while the remaining leading half is still larger than the reversed trailing half, it peels the last digit with remainder-ten and appends it to the reverse. Even-length numbers succeed when the two halves are equal.

Odd-length numbers succeed when the leading half equals the reverse with the middle digit dropped. Numbers that end in zero cannot be palindromes unless the number itself is zero, because a leading zero is never written. Negative inputs skip the loop and return false.

Where a yes-or-no palindrome check earns its keep

Students meet palindromic numbers when they first reverse digits, when they study Lychrel candidates, and when contest problems ask whether a handle, a ticket number, or a generated identifier is symmetric. Teachers can generate answer keys for worksheets without trusting a calculator that silently drops a minus sign or treats ten as a palindrome because it looks at the absolute value.

Developers use the same contract to validate sample data for number-theory libraries, to gate property tests on random integer generators, or to pre-check that a seed is palindromic before a demonstration step that assumes a symmetric digit string. On this page the work runs entirely in your browser.

Pair it with a multi-base palindrome listing when you need every radix that makes n symmetric, with a perfect-square checker when you need membership in n squared, and with prime factorization when you need the prime signature rather than the digit symmetry of the same integer.